Consumption Smoothing and Discounting in Infinite-Horizon, Discrete-Choice Problems

2021 ◽  
Author(s):  
Jeremy Kettering ◽  
Asen Kochov
Keyword(s):  
Discrete Choice ◽  
Preference Relation ◽  
Infinite Horizon ◽  
Comparative Statics ◽  
Consumption Smoothing ◽  
Infinitely Divisible ◽  
Continuous Utility ◽  
The Standard Model ◽  
Endogenous Discounting ◽  
Over Time

Suppose the consumption space is discrete. Our first contribution is a technical result showing that any continuous utility function of any stationary preference relation over infinite consumption streams has convex range, provided that the agent is sufficiently patient. Putting the result to use, we consider a model of endogenous discounting (a generalization of the standard model with geometric discounting) and show the uniqueness of the consumption-dependent discount factor as well as the cardinal uniqueness of utility. Comparative statics are then provided to substantiate the uniqueness. For instance, we show that, as in the more familiar case of an infinitely divisible good, the cardinal uniqueness of utility captures an agent’s desire to smooth consumption over time.

scholarly journals Dynamic Attribute-Level Best Worst Discrete Choice Experiments

2019 ◽  
Vol 11 (2) ◽  
pp. 1
Author(s):  
Amanda Working ◽  
Mohammed Alqawba ◽  
Norou Diawara
Keyword(s):  
Decision Maker ◽  
Discrete Choice ◽  
Dynamic Modelling ◽  
Choice Experiments ◽  
Discrete Choice Experiments ◽  
Systems Research ◽  
Decision Choices ◽  
Markov Decision ◽  
Transportation Research ◽  
Over Time

Dynamic modelling of decision maker choice behavior of best and worst in discrete choice experiments (DCEs) has numerous applications. Such models are proposed under utility function of decision maker and are used in many areas including social sciences, health economics, transportation research, and health systems research. After reviewing references on the study of such experiments, we present example in DCE with emphasis on time dependent best-worst choice and discrimination between choice attributes. Numerical examples of the dynamic DCEs are simulated, and the associated expected utilities over time of the choice models are derived using Markov decision processes. The estimates are computationally consistent with decision choices over time.

In Defense of Comparative Statics: Specifying Empirical Tests of Models of Strategic Interaction

2007 ◽  
Vol 15 (4) ◽  
pp. 465-482 ◽  
Author(s):  
Clifford J. Carrubba ◽  
Amy Yuen ◽  
Christopher Zorn
Keyword(s):  
Discrete Choice ◽  
Strategic Behavior ◽  
Formal Model ◽  
Comparative Statics ◽  
Formal Models ◽  
Likelihood Estimator ◽  
Alternative Methodology ◽  
Empirical Tests ◽  
Parametric Relationships ◽  
Traditional Approaches

Beginning in 1999, Curtis Signorino challenged the use of traditional logits and probits analysis for testing discrete-choice, strategic models. Signorino argues that the complex parametric relationships generated by even the simplest strategic models can lead to wildly inaccurate inferences if one applies these traditional approaches. In their stead, Signorino proposes generating stochastic formal models, from which one can directly derive a maximum likelihood estimator. We propose a simpler, alternative methodology for theoretically and empirically accounting for strategic behavior. In particular, we propose carefully and correctly deriving one's comparative statics from one's formal model, whether it is stochastic or deterministic does not particularly matter, and using standard logit or probit estimation techniques to test the predictions. We demonstrate that this approach performs almost identically to Signorino's more complex suggestion.

OPTIMAL EXIT FROM A PROJECT WITH NOISY RETURNS

2003 ◽  
Vol 17 (4) ◽  
pp. 435-458 ◽  
Author(s):  
Reade Ryan ◽  
Steven A. Lippman
Keyword(s):  
Posterior Probability ◽  
Stopping Time ◽  
Investment Project ◽  
Comparative Statics ◽  
Critical Number ◽  
High State ◽  
Profit Rate ◽  
Brownian Motion With Drift ◽  
Changes Over Time ◽  
Over Time

We consider the problem of selecting a stopping time τ which determines when to exit an investment project when the project's cumulative profit up to time t is Xt, where {Xt : t ≥ 0} is a Brownian motion with drift μ and variance σ2. The profit rate μ never changes over time, but μ is not directly observable. Specifically, μ takes the value μH > 0 when in the high state and μL < 0 when in the low state, and the initial probability p0 that the project is in the high state is known. The decision-maker seeks to maximize the expected discounted profit up to time τ. Using the theory of stochastic differential equations, we show that it is optimal to exit only when the posterior probability Pt of being in the high state falls below a critical number p*, and we produce a simple, closed form for p*. Our most surprising comparative-statics result is that the expected discounted profit increases with |μL|, provided |μL| is large.

scholarly journals Comparative Statics and Perfect Foresight in Infinite Horizon Economies

Econometrica ◽  
1985 ◽  
Vol 53 (2) ◽  
pp. 433 ◽  
Author(s):  
Timothy J. Kehoe ◽  
David K. Levine
Keyword(s):  
Infinite Horizon ◽  
Comparative Statics ◽  
Perfect Foresight

scholarly journals A Discounted-Cost Continuous-Time Flexible Manufacturing and Operator Scheduling Model Solved by Deconvexification Over Time

1995 ◽  
Vol 9 (1) ◽  
pp. 65-98
Author(s):  
B. Curtis Eaves ◽  
Uriel G. Rothblum
Keyword(s):  
Continuous Time ◽  
Flexible Manufacturing ◽  
Infinite Horizon ◽  
Solution Procedure ◽  
Linear Program ◽  
Discounted Cost ◽  
Scheduling Model ◽  
Availability Constraints ◽  
Operator Assignment ◽  
Over Time

A discounted-cost, continuous-time, infinite-horizon version of a flexible manufacturing and operator scheduling model is solved. The solution procedure is to convexify the discrete operator-assignment constraints to obtain a linear program and then to regain the discreteness and obtain an approximate manufacturing schedule by deconvexification of the solution of the linear program over time. The strong features of the model are the accommodation of linear inequality relations among the manufacturing activities and the discrete manufacturing scheduling, whereas the weak features are intra-period relaxation of inventory availability constraints and the absence of inventory costs, setup times, and setup charges.

scholarly journals Intertemporal Price Discrimination: Dynamic Arrivals and Changing Values

2016 ◽  
Vol 106 (11) ◽  
pp. 3275-3299 ◽  
Author(s):  
Daniel F. Garrett
Keyword(s):  
Price Discrimination ◽  
Infinite Horizon ◽  
Durable Good ◽  
Intertemporal Price Discrimination ◽  
Profit Maximizing ◽  
Dynamic Arrivals ◽  
Over Time

We study the profit-maximizing price path of a monopolist selling a durable good to buyers who arrive over time and whose values for the good evolve stochastically. The setting is completely stationary with an infinite horizon. Contrary to the case with constant values, optimal prices fluctuate with time. We argue that consumers’ randomly changing values offer an explanation for temporary price reductions that are often observed in practice. (JEL D82)

scholarly journals A novel cost framework reveals evidence for competitive selection in the evolution of complex traits during plant domestication

2020 ◽  
Author(s):  
Robin G Allaby ◽  
Chris J Stevens ◽  
Dorian Q Fuller
Keyword(s):  
Grain Size ◽  
Standard Model ◽  
Complex Traits ◽  
Selection Intensity ◽  
Model Framework ◽  
Competitive Selection ◽  
The Standard Model ◽  
Fundamental Insight ◽  
Insight Into ◽  
Over Time

AbstractMost models of selection incorporate some notion of an environmental degradation in which the majority of the population becomes less fit with respect to a character resulting in a pressure to adapt. Such models have been variously associated with an adaptation cost, the substitution load. Conversely, adaptative mutations that represent an improvement in fitness in the absence of environmental change have generally been assumed to be associated with negligible cost. However, such adaptations could represent a competitive advantage that diminishes resource availability for others and so induce a cost. This type of adaptation in the form of seedling competition has been suggested as a mechanism for increases in seed size during domestication. Here we present a novel cost framework for competitive selection that demonstrates significant differences in behaviour to environmental based selection in typical initial selection intensity and intensity over time. We show that selection intensity over time in grain size metrics of nine archaeological crops increases in one to several episodes fitting closely to the competitive selection model of single large effect alleles, but surprisingly in direct contrast to the expectations of the standard model of stabilizing selection. While size trait changes ultimately slow down in crops over time as expected from pleiotropic constraints expressed in the standard model, the mechanism outlined here shows possible complexities within the environmental based mode of shifting optimums in the standard model and a fundamental insight into the factors driving domestication.Significance statementWe present here a new model framework for selection based on direct competition between individuals rather than the more conventional approach of individual’s fitness being measured against an environmental gradient. The model explains patterns of increasing selection intensity seen in archaeological grain sizes of nine domesticated crops that otherwise contradict the expectations of shifting stabilising selection of complex traits. We show that grain size increases seen across domesticated crops are consistent with spontaneous competition between seedlings under cultivation for resources and so reveal a fundamental insight into the mechanism of plant adaptation to the human environment.

scholarly journals MULTI-ARMED BANDITS UNDER GENERAL DEPRECIATION AND COMMITMENT

2014 ◽  
Vol 29 (1) ◽  
pp. 51-76 ◽  
Author(s):  
Wesley Cowan ◽  
Michael N. Katehakis
Keyword(s):  
State Space ◽  
Infinite Horizon ◽  
Constant Factor ◽  
Finite Collection ◽  
Time Step ◽  
Discount Factors ◽  
Stochastic Duration ◽  
Statistical Experiments ◽  
Step Over ◽  
Over Time

Generally, the multi-armed has been studied under the setting that at each time step over an infinite horizon a controller chooses to activate a single process or bandit out of a finite collection of independent processes (statistical experiments, populations, etc.) for a single period, receiving a reward that is a function of the activated process, and in doing so advancing the chosen process. Classically, rewards are discounted by a constant factor β∈(0, 1) per round.In this paper, we present a solution to the problem, with potentially non-Markovian, uncountable state space reward processes, under a framework in which, first, the discount factors may be non-uniform and vary over time, and second, the periods of activation of each bandit may be not be fixed or uniform, subject instead to a possibly stochastic duration of activation before a change to a different bandit is allowed. The solution is based on generalized restart-in-state indices, and it utilizes a view of the problem not as “decisions over state space” but rather “decisions over time”.

scholarly journals IDENTIFICATION OF DISCRETE CHOICE DYNAMIC PROGRAMMING MODELS WITH NONPARAMETRIC DISTRIBUTION OF UNOBSERVABLES

2016 ◽  
Vol 33 (3) ◽  
pp. 551-577 ◽  
Author(s):  
Le-Yu Chen
Keyword(s):  
Dynamic Programming ◽  
Discrete Choice ◽  
Dynamic Models ◽  
Structural Parameters ◽  
Infinite Horizon ◽  
Sufficient Conditions ◽  
State Variables ◽  
Structural Dynamic ◽  
Continuous Choice ◽  
Exclusion Restrictions

This paper presents semiparametric identification results for the Rust (1994) class of discrete choice dynamic programming (DCDP) models. We develop sufficient conditions for identification of the deep structural parameters for the case where the per-period utility function ascribed to one choice in the model is parametric but the distribution of unobserved state variables is nonparametric. The proposed identification strategy does not rely on availability of the terminal period data and can therefore be applied to infinite horizon structural dynamic models. Identifying power comes from assuming that the agent’s per-period utilities admit continuous choice-specific state variables that are observed with sufficient variation and satisfy certain conditional independence assumptions on the joint time series of observables. These conditions allow us to formulate exclusion restrictions for identifying the primitive structural functions of the model.

scholarly journals Sample-based longitudinal discrete choice experiments: preferences for electric vehicles over time

2021 ◽  
Author(s):  
Katharina Keller ◽  
Christian Schlereth ◽  
Oliver Hinz
Keyword(s):  
Discrete Choice ◽  
Electric Vehicles ◽  
Choice Experiment ◽  
State Of The Art ◽  
Statistical Significance ◽  
Choice Experiments ◽  
Hierarchical Bayes ◽  
Discrete Choice Experiments ◽  
Cross Sectional ◽  
Over Time

AbstractDiscrete choice experiments have emerged as the state-of-the-art method for measuring preferences, but they are mostly used in cross-sectional studies. In seeking to make them applicable for longitudinal studies, our study addresses two common challenges: working with different respondents and handling altering attributes. We propose a sample-based longitudinal discrete choice experiment in combination with a covariate-extended hierarchical Bayes logit estimator that allows one to test the statistical significance of changes. We showcase this method’s use in studies about preferences for electric vehicles over six years and empirically observe that preferences develop in an unpredictable, non-monotonous way. We also find that inspecting only the absolute differences in preferences between samples may result in misleading inferences. Moreover, surveying a new sample produced similar results as asking the same sample of respondents over time. Finally, we experimentally test how adding or removing an attribute affects preferences for the other attributes.

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